Based on the photos that are on the sellers site alone, the paint actually doesn't look too bad, so maybe a good polish will bring it up. Like any red painted with "old" paint, it'll probably need regular polishing to keep it sharp. If you do put new carpets in, I doubt they will be affected by the UK sun in the same way as, say, a car based in Florida! That goes for the leather and trim parts. Clearly it needs new seat covers, and they should stay fresh for years.
I suspect that they be other more pressing items to consider though, the rear suspension looks to need some inspection, and there will be a good deal of tidying and examination needed under the bonnet. and yes, there is the chassis etc.... Not wanting to put a damper on your hopes, but you may be a while before you are at a car show.
You mentioned in one of your other threads that you have most of the info needed for your viewing - I assume you have a copy of the club's C3 Buyers Guide?
By the way, I noticed the cover/locking ring from the distributor cap is laying in the wiper well - you may want to put that somewhere safe when you view the car, in case you buy it and need it later!
